This article considers the problem of classifying individuals in a dataset of diverse psychosis spectrum conditions, including persons with subsyndromal psychotic-like experiences (PLEs) and healthy controls. This task is more challenging than the traditional problem of distinguishing patients with a diagnosed disorder from controls using brain network features, since the neurobiological differences between PLE individuals and healthy persons are less pronounced. Further, examining a transdiagnostic sample compared to controls is concordant with contemporary approaches to understanding the full spectrum of neurobiology of psychoses. We consider both support vector machines (SVMs) and graph convolutional networks (GCNs) for classification, with a variety of edge selection methods for processing the inputs. We also employ the MultiVERSE algorithm to generate network embeddings of the functional and structural networks for each subject, which are used as inputs for the SVMs. The best models among SVMs and GCNs yielded accuracies >63%. Investigation of network connectivity between persons with PLE and controls identified a region within the right inferior parietal cortex, called the PGi, as a central region for communication among modules (network hub). Class activation mapping revealed that the PLE group had salient regions in the dorsolateral prefrontal, orbital and polar frontal cortices, and the lateral temporal cortex, whereas the controls did not. Our study demonstrates the potential usefulness of deep learning methods to distinguish persons with subclinical psychosis and diagnosable disorders from controls. In the long term, this could help improve accuracy and reliability of clinical diagnoses, provide neurobiological bases for making diagnoses, and initiate early intervention strategies.